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Simplifying -11x2 + 3x + -7x2 + 2 = 0 Reorder the terms: 2 + 3x + -11x2 + -7x2 = 0 Combine like terms: -11x2 + -7x2 = -18x2 2 + 3x + -18x2 = 0 Solving 2 + 3x + -18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -18 the coefficient of the squared term: Divide each side by '-18'. -0.1111111111 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + -0.1666666667x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + -0.1666666667x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + -0.1666666667x + x2 = 0 + 0.1111111111 -0.1666666667x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 -0.1666666667x + x2 = 0.1111111111 The x term is -0.1666666667x. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667x + 0.006944444447 + x2 = 0.1111111111 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 0.1111111111 + 0.006944444447 Combine like terms: 0.1111111111 + 0.006944444447 = 0.118055555547 0.006944444447 + -0.1666666667x + x2 = 0.118055555547 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 0.118055555547 Calculate the square root of the right side: 0.343592135 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 0.343592135 and -0.343592135.Subproblem 1
x + -0.08333333335 = 0.343592135 Simplifying x + -0.08333333335 = 0.343592135 Reorder the terms: -0.08333333335 + x = 0.343592135 Solving -0.08333333335 + x = 0.343592135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = 0.343592135 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 0.343592135 + 0.08333333335 x = 0.343592135 + 0.08333333335 Combine like terms: 0.343592135 + 0.08333333335 = 0.42692546835 x = 0.42692546835 Simplifying x = 0.42692546835Subproblem 2
x + -0.08333333335 = -0.343592135 Simplifying x + -0.08333333335 = -0.343592135 Reorder the terms: -0.08333333335 + x = -0.343592135 Solving -0.08333333335 + x = -0.343592135 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = -0.343592135 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -0.343592135 + 0.08333333335 x = -0.343592135 + 0.08333333335 Combine like terms: -0.343592135 + 0.08333333335 = -0.26025880165 x = -0.26025880165 Simplifying x = -0.26025880165Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.42692546835, -0.26025880165}
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